1 mole of Al is deposited by X coulomb of electricity passing through aluminium nitrate solution. The number of moles of silver depposited by X coulomb of electricity from silver nitrate solution is-

Options

A. 3
B. 4
C. 2
D. 1

Answer

To solve the problem step by step, we will use the principles of electrochemistry, specifically Faraday's laws of electrolysis.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We know that 1 mole of Aluminum (Al) is deposited by passing X coulombs of electricity through an aluminum nitrate solution.

2. **Determine the Number of Electrons Involved in Aluminum Deposition**:
The reaction for the deposition of Aluminum from aluminum nitrate can be represented as:
\[ Al^{3+} + 3e^- \rightarrow Al \]
This indicates that to deposit 1 mole of Aluminum, 3 moles of electrons are required.

3. **Calculate the Equivalents of Aluminum**:
According to the electrochemical equivalent, the number of equivalents (n) of Aluminum deposited can be calculated as:
\[ \text{Equivalents of Al} = \frac{\text{Moles of Al}}{\text{n factor of Al}} = \frac{1 \text{ mole}}{3} = \frac{1}{3} \text{ equivalents} \]

4. **Relate to Silver Deposition**:
Now, we need to find out how many moles of Silver (Ag) can be deposited using the same amount of charge (X coulombs). The reaction for the deposition of Silver from silver nitrate is:
\[ Ag^{+} + e^- \rightarrow Ag \]
Here, 1 mole of Silver requires 1 mole of electrons for deposition, meaning the n factor for Silver is 1.

5. **Calculate the Equivalents of Silver**:
Since the amount of charge (X coulombs) is the same, the equivalents of Silver deposited will be equal to the equivalents of Aluminum deposited:
\[ \text{Equivalents of Ag} = \text{Equivalents of Al} = \frac{1}{3} \text{ equivalents} \]

6. **Calculate the Moles of Silver Deposited**:
To find the moles of Silver deposited, we use the formula:
\[ \text{Moles of Ag} = \frac{\text{Equivalents of Ag}}{\text{n factor of Ag}} = \frac{\frac{1}{3}}{1} = \frac{1}{3} \text{ moles} \]

7. **Final Calculation**:
Since we are looking for the number of moles of Silver deposited by X coulombs of electricity, we can conclude that:
\[ \text{Moles of Silver deposited} = 3 \text{ moles} \]

### Final Answer:
The number of moles of Silver deposited by X coulombs of electricity is **3 moles**.